在数列问题中,经常需要由递推公式求出通项公式,用通项公式解决问题.但是笔者在教学实践中发现,有些数列问题却需要由通项公式求出递推公式,用递推公式解决问题.下面试举几例,以引起读者对此类问题的足够重视. 例1 设n≥2,且n∈N.证明: (1992年日本奥林匹克试题) In the series of problems, it is often necessary to derive the general term formula from the recursive formula and use the general term formula to solve the problem. However, in the teaching practice, the author discovered that some sequence problems need to find the recurrence formula from the general term formula, and use recursion to solve the problem. The formula solves the problem. Here are a few examples to give readers enough attention to this type of problem. Example 1 Let n≥2 and n∈N. Prove that: (Japan Olympics 1992)